Page 36 - Bird R.B. Transport phenomena

§1.3 Pressure and Temperature Dependence of Viscosity 21

Flow Fig. 1.2-3 The flow in a converging duct is an example of a situation
in which the normal stresses are not zero. Since v z is a function of
r and z, the normal-stress component T = -2\x{dvJdz) is nonzero.
ZZ
Also, since v depends on r and z, the normal-stress component
r
T = -2ix(dv /dr) is not equal to zero. At the wall, however, the
n
r
v z (r) normal stresses all vanish for fluids described by Eq. 1.2-7 provided
that the density is constant (see Example 3.1-1 and Problem 3C.2).

§13 PRESSURE AND TEMPERATURE DEPENDENCE
OF VISCOSITY

Extensive data on viscosities of pure gases and liquids are available in various science
and engineering handbooks. 1 When experimental data are lacking and there is not time
to obtain them, the viscosity can be estimated by empirical methods, making use of other
data on the given substance. We present here a corresponding-states correlation, which fa-
cilitates such estimates and illustrates general trends of viscosity with temperature and
pressure for ordinary fluids. The principle of corresponding states, which has a sound
scientific basis, 2 is widely used for correlating equation-of-state and thermodynamic
data. Discussions of this principle can be found in textbooks on physical chemistry and
thermodynamics.
The plot in Fig. 1.3-1 gives a global view of the pressure and temperature dependence
of viscosity. The reduced viscosity /г,. = д//х с is plotted versus the reduced temperature T r
= T/T c for various values of the reduced pressure p r = p/p . A "reduced" quantity is one
c
that has been made dimensionless by dividing by the corresponding quantity at the criti-
cal point. The chart shows that the viscosity of a gas approaches a limit (the low-density
limit) as the pressure becomes smaller; for most gases, this limit is nearly attained at 1 atm
pressure. The viscosity of a gas at low density increases with increasing temperature,
whereas the viscosity of a liquid decreases with increasing temperature.
Experimental values of the critical viscosity /x f are seldom available. However, fi c
may be estimated in one of the following ways: (i) if a value of viscosity is known at a
given reduced pressure and temperature, preferably at conditions near to those of

J. A. Schetz and A. E. Fuhs (eds.), Handbook of Fluid Dynamics and Fluid Machinery, Wiley-
1
Interscience, New York (1996), Vol. 1, Chapter 2; W. M. Rohsenow, J. P. Hartnett, and Y. I. Cho, Handbook
of Heat Transfer, McGraw-Hill, New York, 3rd edition (1998), Chapter 2. Other sources are mentioned in
fn. 4 of §1.1.
2
J. Millat, J. H. Dymond, and C. A. Nieto de Castro (eds.), Transport Properties of Fluids, Cambridge
University Press (1996), Chapter 11, by E. A. Mason and F. J. Uribe, and Chapter 12, by M. L. Huber and
H. M. M. Hanley.